﻿using System.Collections.Generic;

namespace ProblemsSet
{
    public class Problem_58 : BaseProblem
    {
        public override object GetResult()
        {
            var res = 1;
            var q = 0;
            while (true)
            {
                res = res + 2;
                var sq = res*res;
                if (MathLogic.IsPrimeNumber(sq - 3 * res + 3)) q++;
                if (MathLogic.IsPrimeNumber(sq - res + 1)) q++;
                if (MathLogic.IsPrimeNumber(sq - 2 * res + 2)) q++;
                
                double r = 100*(double)q/(2*res -1);
                if (r < 10) return res;
            }
        }

        public override string Problem
        {
            get
            {
                return @"Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.

37 36 35 34 33 32 31
38 17 16 15 14 13 30
39 18  5  4  3 12 29
40 19  6  1  2 11 28
41 20  7  8  9 10 27
42 21 22 23 24 25 26
43 44 45 46 47 48 49

It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13  62%.

If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?";
            }
        }

        public override bool IsSolved
        {
            get
            {
                return true;
            }
        }

        public override object Answer
        {
            get
            {
                return 26241;
            }
        }

    }
}
